The difference compound and simple rates of interest on? 10000 for 3 yr at 5% per annum is

Options

A. ? 76.25
B. ? 76.75
C. ? 76.50
D. ? 76

Answer

To find the difference between the compound interest and simple interest on a principal amount of ₹10,000 for 3 years at an interest rate of 5% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount = ₹10,000
- \( R \) = Rate of interest = 5%
- \( T \) = Time in years = 3

Substituting the values:
\[ SI = \frac{10000 \times 5 \times 3}{100} \]
\[ SI = \frac{150000}{100} = ₹1500 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount = ₹10,000
- \( R \) = Rate of interest = 5%
- \( T \) = Time in years = 3

Substituting the values:
\[ A = 10000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 10000 \left(1 + 0.05\right)^3 \]
\[ A = 10000 \left(1.05\right)^3 \]
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substituting back:
\[ A = 10000 \times 1.157625 = ₹11576.25 \]

Now, calculate the Compound Interest:
\[ CI = A - P \]
\[ CI = 11576.25 - 10000 = ₹1576.25 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = CI - SI \]
\[ \text{Difference} = 1576.25 - 1500 = ₹76.25 \]

### Final Answer
The difference between the compound interest and simple interest is **₹76.25**.

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